When I was in the market for a new car in 2008, one of the cars I test-drove had a continuously variable transmission (CVT). Rather than changing gears (whether automatically or manually), the transmission in this car contained two pulleys connected by a steel drive belt. The pulleys were made in such a way that their diameter could be adjusted. If the pulley connected to the engine was small and the one connected to the wheels was large the car would move as if in a low gear. If the engine pulley was large and the wheel pulley small the car would move as if in a high gear. The car would move smoothly between these two extremes depending on the driving conditions at the time.
Let
r be the radius of the engine pulley
s be the radius of the wheel pulley
l be the length of the belt
Suppose that in a particular CVT, the largest radius of either pulley is 6cm and the smallest is 3cm. The distance between the pulley centres is 13cm.
What length l must the belt be for the case when one pulley has a radius of 6cm and the other 3cm?
Given that the length of the belt does not change, how do you expect the two radii to change? Make a conjecture about the relationship you expect to find between them.
Using the length determined in the first question, determine the radius of the two pulleys when they are both the same size.
Determine the radius of the wheel pulley when the engine pulley is 4cm in radius.
Compare your results with your conjecture. Do they support or refute it?
Are you able to determine the radius of the engine pulley r cm when the wheel pulley has a radius of s cm?
Skills Required
Depending on your approach, this problem may need the following new skills:
Radian measure of angles
Arc length
Solutions
Create a page for your solution here by putting the problem title and your name in square brackets like this:
Then save this page and click on the new link you have created to go to the new page. Edit that page and put your solution there. Sign it at the bottom with four tildes (i.e. ~). This will automatically turn into a date-stamped signature like this: - glenprideaux Jan 15, 2009
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This page has been edited 2 times. The last modification was made by - glenprideaux on Jan 15, 2009 3:14 pm
Continuously Variable Transmission
Let
Suppose that in a particular CVT, the largest radius of either pulley is 6cm and the smallest is 3cm. The distance between the pulley centres is 13cm.
Skills Required
Depending on your approach, this problem may need the following new skills:Solutions
Create a page for your solution here by putting the problem title and your name in square brackets like this:Then save this page and click on the new link you have created to go to the new page. Edit that page and put your solution there. Sign it at the bottom with four tildes (i.e. ~). This will automatically turn into a date-stamped signature like this: -
For help editing these pages, see Editing.
This page has been edited 2 times. The last modification was made by
-